FFT-Based Fast Computation of Multivariate Kernel Estimators with Unconstrained Bandwidth Matrices

The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes the fast Fourier transform. Unfortunately, the existing FFT-based solution suffers from a serious limitation, as it can accurately operate only with the constrained (i.e., diagonal) multivariate bandwidth matrices. In this paper we describe the problem and give a satisfactory solution. The proposed solution may be successfully used also in other research problems, for example for the fast computation of the optimal bandwidth for KDE.Comment: 10 pages, 1 figure, R source code

FPGA-Based Bandwidth Selection for Kernel Density Estimation Using High Level Synthesis Approach

FPGA technology can offer significantly hi\-gher performance at much lower power consumption than is available from CPUs and GPUs in many computational problems. Unfortunately, programming for FPGA (using ha\-rdware description languages, HDL) is a difficult and not-trivial task and is not intuitive for C/C++/Java programmers. To bring the gap between programming effectiveness and difficulty the High Level Synthesis (HLS) approach is promoting by main FPGA vendors. Nowadays, time-intensive calculations are mainly performed on GPU/CPU architectures, but can also be successfully performed using HLS approach. In the paper we implement a bandwidth selection algorithm for kernel density estimation (KDE) using HLS and show techniques which were used to optimize the final FPGA implementation. We are also going to show that FPGA speedups, comparing to highly optimized CPU and GPU implementations, are quite substantial. Moreover, power consumption for FPGA devices is usually much less than typical power consumption of the present CPUs and GPUs.Comment: 23 pages, 6 figures, extended version of initial pape